A model of persistent breaking of continuous symmetry

Abstract

We consider a UV-complete field-theoretic model in general dimensions, including $d=2+1$, that exhibits spontaneous breaking of continuous symmetry, persisting to arbitrarily large temperatures. Our model consists of two copies of the long-range vector models, with $O(m)$ and $O(N-m)$ global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for $N\ge 6$ that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Our work generalizes recent results, which considered the particular case of $m=1$ and reported persistent breaking of the discrete ${\mathbb{Z}}_2=O(1)$. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite $N$.

V2: references and minor changes in the text

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• RG studies of scalar-field models of long-range interactions
• Universal thermalization dynamics in (1+1)d QFTs
• The quest for a conifold conformal order